Composition independence in compound games: a characterization of the Banzhaf power index and the Banzhaf value

Ori Haimanko ()

International Journal of Game Theory, 2019, vol. 48, issue 3, No 2, 755-768

Abstract: Abstract We introduce the axiom of composition independence for power indices and value maps. In the context of compound (two-tier) voting, the axiom requires the power attributed to a voter to be independent of the second-tier voting games played in all constituencies other than that of the voter. We show that the Banzhaf power index is uniquely characterized by the combination of composition independence, four semivalue axioms (transfer, positivity, symmetry, and dummy), and a mild efficiency-related requirement. A similar characterization is obtained as a corollary for the Banzhaf value on the space of all finite games (with transfer replaced by additivity).

Keywords: Simple games; Compound games; Banzhaf power index; Banzhaf value; Composition property; Semivalues; Transfer; Symmetry; Positivity; Dummy (search for similar items in EconPapers)
JEL-codes: C71 D72 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00182-019-00660-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
Working Paper: COMPOSITION INDEPENDENCE IN COMPOUND GAMES: A CHARACTERIZATION OF THE BANZHAF POWER INDEX AND THE BANZHAF VALUE (2017)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:48:y:2019:i:3:d:10.1007_s00182-019-00660-w

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2

DOI: 10.1007/s00182-019-00660-w

Access Statistics for this article

International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel

More articles in International Journal of Game Theory from Springer, Game Theory Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().